The idea of using winglets to reduce induced drag on aircraft wings was studied by Richard Whitcomb of NASA and others in the 1970s. Since then, a number of variations on this idea have been patented (see, for example, U.S. Pat. No. 4,205,810 to Ishimitsu and U.S. Pat. No. 5,275,358 to Goldhammer, et al.). In addition, a number of winglet variations are currently in service. Such winglets include horizontal span extensions, like those of the Boeing 767-400 and 777-400 aircraft, and aft-swept span extensions canted upward or downward at various angles. These devices can be added to a new wing during the initial design phase of an all-new aircraft, or they can be added to an existing wing as a retrofit or during development of a derivative model.
The induced drag of a wing or a wing/winglet combination can be calculated with reasonable accuracy using the classic “Trefftz plane theory.” According to this theory, the induced drag of an aircraft wing depends only on the trailing edge trace of the “lifting system” (i.e., the wing plus tip device), as viewed directly from the front or rear of the wing, and the “spanload.” The spanload is the distribution of aerodynamic load perpendicular to the trailing edge trace of the wing. (Aerodynamicists often refer to this aerodynamic load distribution as “lift,” even though the load is not vertical when the trailing edge trace is tilted from horizontal.) Adding a winglet or other wing tip device to a wing changes both the trailing edge trace (i.e., the “Trefftz-plane geometry”) and the spanload. As a result, adding such a device also changes the induced drag on the wing.
For a given Trefftz-plane geometry and a given total vertical lift, there is generally one spanload that gives the lowest possible induced drag. This is the “ideal spanload,” and the induced drag that results from the ideal spanload is the “ideal induced drag.” For a flat wing where the Trefftz-plane geometry is a horizontal line, the ideal spanload is elliptical. Conventional aircraft wings without winglets are close enough to being flat in the Trefftz-plane that their ideal spanloads are very close to elliptical. For conventional aircraft wings having vertical or near-vertical winglets (i.e., nonplanar lifting systems), the ideal spanload is generally not elliptical, but the ideal spanload can be easily calculated from conventional wing theory.
Conventional aircraft wings are generally not designed with ideal or elliptical spanloads. Instead, they are designed with compromised “triangular” spanloads that reduce structural bending loads at the wing root. Such designs trade a slight increase in induced drag for a reduction in airframe weight. The degree of compromise varies considerably from one aircraft model to another. To produce such a triangular spanload, the wing tip is typically twisted to produce “wash-out.” Wash-out refers to a wing tip that is twisted so that the leading edge moves downward and the trailing edge moves upward relative to the wing root. Washing out the wing tip in this manner lowers the angle of attack of the wing tip with respect to the wing root, thereby reducing the lift distribution toward the wing tip.
Conventional winglets are typically swept aft to avoid detrimental shock wave interaction between the wing and the winglet. When such a winglet is added to an existing or “baseline” wing, the resulting spanload differs from the ideal spanload because the baseline wing was originally designed to operate efficiently without a winglet. This difference is accentuated by the compromised triangular lift distribution generally associated with conventional wings. As a result, the benefit of adding the winglet often falls far short of the benefit theoretically available from the ideal spanload.
Technical Report AFFDL-TR-76-6, entitled “Design and Analysis of Winglets for Military Aircraft,” and published by the Boeing Commercial Airplane Company in 1976, provides the results from a parametric study of various types of winglets. The study included a range of winglet sweep angles, including forward sweep angles (see, for example, FIG. 43 of the Report). Apparently, however, in this study the winglets were only combined with flat (i.e., non-washed-out) wings having optimum, or nearly optimum, elliptical spanloads. The winglets were apparently not combined with conventional washed-out wings having triangular spanloads. As a result, this study failed to identify any significant benefits associated with forward swept winglets.